In this work, we study estimation problems in nonlinear mechanical systems subject to non-stationary and unknown excitation, which are common and critical problems in design and health management of mechanical systems. A primary-auxiliary model scheduling procedure based on time-domain transmissibilities is proposed and performed under switching linear dynamics: In addition to constructing a primary transmissibility family from the pseudo-inputs to the output during the offline stage, an auxiliary transmissibility family is constructed by further decomposing the pseudo-input vector into two parts. The auxiliary family enables to determine the unknown working condition at which the system is currently running at, and then an appropriate transmissibility from the primary transmissibility family for estimating the unknown output can be selected during the online estimation stage. As a result, the proposed approach offers a generalizable and explainable solution to the signal estimation problems in nonlinear mechanical systems in the context of switching linear dynamics with unknown inputs. A real-world application to the estimation of the vertical wheel force in a full vehicle system are, respectively, conducted to demonstrate the effectiveness of the proposed method. During the vehicle design phase, the vertical wheel force is the most important one among Wheel Center Loads (WCLs), and it is often measured directly with expensive, intrusive, and hard-to-install measurement devices during full vehicle testing campaigns. Meanwhile, the estimation problem of the vertical wheel force has not been solved well and is still of great interest. The experimental results show good performances of the proposed method in the sense of estimation accuracy for estimating the vertical wheel force.
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